SOLUTION: How do I prove (cosx+cotx)/(sinx+1)= Cotx Thank you

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Question 870244: How do I prove
(cosx+cotx)/(sinx+1)= Cotx
Thank you
Found 2 solutions by josgarithmetic, mananth:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Start with substituting the definitions for cotangent in the left side member.
%28cos%28x%29%2Bcos%28x%29%2Fsin%28x%29%29%2F%28sin%28x%29%2B1%29

%28cos%28x%29sin%28x%29%2Fsin%28x%29%2Bcos%28x%29%2Fsin%28x%29%29%2F%28sin%28x%29%2B1%29

%28%28cos%28x%29sin%28x%29%2Bcos%28x%29%29%2Fsin%28x%29%29%2F%28sin%28x%29%2B1%29

%28cos%28x%29sin%28x%29%2Bcos%28x%29%29%2F%28sin%28x%29%28sin%28x%29%2B1%29%29

%28cos%28x%29sin%28x%29%2Bcos%28x%29%29%2F%28sin%28x%29%28sin%28x%29%2B1%29%29,

%28cos%28x%29sin%28x%29%2Bcos%28x%29%29%2F%28sin%28x%29%28sin%28x%29%2B1%29%29

%28cos%28x%29%28sin%28x%29%2B1%29%29%2F%28sin%28x%29%28sin%28x%29%2B1%29%29



and you see the definition again of cotangent?

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
%28cosx%2Bcotx%29%2F%28sinx%2B1%29=+Cotx

%28cos+x+%2B%28cos+x%2Fsin+x%29%29%2F%28sinx%2B1%29

%28%28sinxcosx%2Bcosx%29%2F%28sinx%29%29%2F%28sinx%2B1%29

(cosx.(1+sinx))/sinx))/(sinx+1)

(cos(1+sinx))/(sinx(1+sinx))
cosx/sinx
cotx